The 2018 World Cup will be hosted in Russia. 32 national teams will be divided into 8 groups. Each group consists of 4 teams. In group matches, each pair (unordered) of teams in the group will have a match. Top 2 teams with the highest score in each group will advance to eighth-finals. Winners of each eighth-final will advance to quarter-finals. Then, the winners of each quarter-final will advance to semi-finals. Eventually, the World Champion will be the winner of the World Final which is played between the two winners of the semi-finals.
Each match is labeled with a match ID sequenced from 1 to 63, with group matches followed by eighth-final matches followed by quarter-final matches followed by semi-finals matches and finally the final match.
_Zhuojie_ is going to watch the 2018 World Cup. Since the World Champion of ACM-ICPC is very rich, he decides to spend 0.01% of his daily salary to buy tickets. However, there are only match IDs on the tickets and the prices are missing. Can you calculate how much _Google_ pays _Zhuojie_ every workday? Note that _Zhuojie_ can buy multiple tickets for one match.
The input starts with one line containing exactly one integer T, the number of test cases.
Each test case contains 3 lines. The first line contains 5 integers, indicating the ticket price for group match, eighth-final match, quarter-final match, semi-final match and the final match. The second line contains one integer N, the number of tickets _Zhuojie_ buys. The third line contains N integers, each indicating the match ID on the ticket.
For each test case, output one line containing "_Case #x: y_" where _x_ is the test case number (starting from 1) and _y_ is daily salary of _Zhuojie_.
## Input
The input starts with one line containing exactly one integer T, the number of test cases.Each test case contains 3 lines. The first line contains 5 integers, indicating the ticket price for group match, eighth-final match, quarter-final match, semi-final match and the final match. The second line contains one integer N, the number of tickets _Zhuojie_ buys. The third line contains N integers, each indicating the match ID on the ticket. 1 ≤ T ≤ 100. 1 ≤ N ≤ 105. . .
## Output
For each test case, output one line containing "_Case #x: y_" where _x_ is the test case number (starting from 1) and _y_ is daily salary of _Zhuojie_.
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**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $, let $ n_k \in \mathbb{Z} $ and $ m_k \in \mathbb{Z}_{\geq 0} $ denote the target position and time in seconds, respectively.
**Constraints**
1. $ 1 \leq T \leq 10^5 $
2. $ -2 \times 10^5 \leq n_k \leq 2 \times 10^5 $
3. $ 0 \leq m_k \leq 2 \times 10^5 $
**Objective**
For each test case $ k $, compute the probability $ P_k $ that a symmetric random walk starting at 0 reaches position $ n_k $ after exactly $ m_k $ steps, where at each step the walker moves $ +1 $ or $ -1 $ with equal probability $ \frac{1}{2} $.
The probability is $ P_k = \frac{\binom{m_k}{\frac{m_k + n_k}{2}}}{2^{m_k}} $ if $ m_k \geq |n_k| $ and $ m_k + n_k $ is even; otherwise $ P_k = 0 $.
Output $ z_k \equiv P_k \pmod{10^9 + 7} $, where $ z_k \in [0, 10^9 + 6] $, interpreted as $ z_k \equiv p \cdot q^{-1} \pmod{10^9 + 7} $ for irreducible fraction $ \frac{p}{q} $.